text: A cylinder (or disk) of radius  is placed in a two-dimensional, incompressible, inviscid flow. The goal is to find the steady velocity vector  and pressure  in a plane, subject to the condition that far from the cylinder the velocity vector (relative to unit vectors  and ) is:
  where  is a constant, and at the boundary of the cylinder
  where  is the vector normal to the cylinder surface. The upstream flow is uniform and has no vorticity. The flow is inviscid, incompressible and has constant mass density . The flow therefore remains without vorticity, or is said to be irrotational, with  everywhere. Being irrotational, there must exist a velocity potential :
  Being incompressible, , so  must satisfy Laplace's equation:
  The solution for  is obtained most easily in polar coordinates  and , related to conventional Cartesian coordinates by  and . In polar coordinates, Laplace's equation is (see Del in cylindrical and spherical coordinates):
  The solution that satisfies the boundary conditions is
  The velocity components in polar coordinates are obtained from the components of  in polar coordinates:
  and
  Being inviscid and irrotational, Bernoulli's equation allows the solution for pressure field to be obtained directly from the velocity field:
  where the constants  and  appear so that  far from the cylinder, where . Using ,
  In the figures, the colorized field referred to as "pressure" is a plot of
  On the surface of the cylinder, or , pressure varies from a maximum of 1 (shown in the diagram in ) at the stagnation points at  and  to a minimum of −3 (shown in ) on the sides of the cylinder, at  and . Likewise,  varies from  at the stagnation points to  on the sides, in the low pressure.